[Paper Review] The MDS Queue: Analysing Latency Performance of Codes and Redundant Requests

Nihar B. Shah, Kangwook Lee+1 more|arXiv (Cornell University)|Nov 23, 2012

Advanced Data Storage Technologies22 references23 citations

TL;DR

This paper introduces the MDS queue model to analyze latency performance in data centers using Maximum Distance Separable (MDS) codes, showing that MDS-coded systems reduce average latency by up to 70% compared to replication. It further demonstrates analytically that redundant requests—sending more requests than needed—can further reduce latency, with optimal performance when all servers are requested, under exponential service times and negligible cancellation costs.

ABSTRACT

In order to scale economically, data centers are increasingly evolving their data storage methods from the use of simple data replication to the use of more powerful erasure codes, which provide the same level of reliability as replication-based methods at a significantly lower storage cost. In particular, it is well known that MaximumDistance-Separable (MDS) codes, such as Reed-Solomon codes, provide the maximum storage efficiency. While the use of codes for providing improved reliability in archival storage systems, where the data is less frequently accessed (or so-called “cold data”), is well understood, the role of codes in the storage of more frequently accessed and active “hot data”, where latency is the key metric, is less clear. In this paper, we study data storage systems based on MDS codes through the lens of queueing theory, and term this the “MDS queue.” We analytically characterize the latency performance of MDS queues, for which we present insightful scheduling policies that form upper and lower bounds to performance, and show that they are quite tight. Extensive simulations using Monte Carlo methods are also provided and used to validate our theoretical analysis. As a side note, our lower-bound analytical method based on the so-called MDS-Reservation(t) queue, represents an elegant practical scheme that requires the maintenance of considerably smaller state, depending on the parameter t, than that of the full-fledged MDS queue (which corresponds to t =∞), and may be of independent interest in practical systems. Comparisons with replication-based systems reveal that codes provide a superior latency-performance (by up to 70%) than replication. The second part of the paper considers an alternative method of (potentially) reducing latency in data centers, that of sending redundant requests. Here, a request is sent to more servers than required, and is deemed served when any requisite number of servers complete service. Several recent works provide empirical evidence of the benefits of redundant requests in various settings, and in this paper, we aim to analytically characterize the situations when can redundant requests actually help. We show that under the MDS queue model (with exponential service times and negligible costs of cancelling jobs), in a replication-based system, the average latency strictly reduces with more redundancy in the requests, and that under a general MDS code, the average latency is minimized when requests are sent to all servers. To the best of our knowledge, these are the first analytical results that prove the benefits of sending redundant requests.

Motivation & Objective

• To understand the latency performance of MDS-coded storage systems in data centers, particularly for frequently accessed 'hot data' where low latency is critical.
• To model and analyze the MDS queue using queueing theory, providing analytical bounds on latency performance.
• To evaluate the impact of redundant requests on reducing latency in both replication-based and MDS-coded systems.
• To determine optimal scheduling policies and redundancy strategies that minimize average latency under realistic assumptions.

Proposed method

• Models data center storage systems using MDS codes as an M/D/1-type queueing system, termed the 'MDS queue', to analyze latency under exponential service times.
• Develops analytical upper and lower bounds on latency performance using scheduling policies, with the lower bound based on the MDS-Reservation(t) queue model.
• Uses Monte Carlo simulations to validate theoretical results and assess performance across varying system parameters.
• Analyzes redundant requests by modeling request forwarding to more servers than required, with completion counted upon any required number of responses.
• Applies queueing theory to prove that increasing redundancy reduces average latency in both replication and MDS-coded systems.
• Introduces the MDS-Reservation(t) queue as a lightweight approximation of the full MDS queue, reducing state maintenance with tunable parameter t.

Experimental results

Research questions

• RQ1 How does the use of MDS codes affect average latency in data center storage systems for hot data?
• RQ2 What are the theoretical upper and lower bounds on latency performance in MDS-coded systems, and how tight are they?
• RQ3 In what scenarios do redundant requests lead to reduced latency, and how does redundancy scale with system parameters?
• RQ4 How does the performance of redundant requests compare between replication-based and MDS-coded systems?
• RQ5 Can analytical models prove the benefits of redundant requests in reducing latency under exponential service times?

Key findings

• MDS-coded storage systems reduce average latency by up to 70% compared to replication-based systems under the same workload conditions.
• The MDS-Reservation(t) queue provides a tight lower bound on latency performance and requires significantly less state than the full MDS queue, especially for small t.
• In replication-based systems, increasing the number of redundant requests strictly reduces average latency, with diminishing returns as redundancy increases.
• For MDS-coded systems, the average latency is minimized when requests are sent to all servers, indicating that full redundancy is optimal.
• Theoretical analysis confirms that redundant requests provide measurable latency benefits in both replication and MDS-coded systems, with the first analytical proof of this effect under exponential service times.
• Simulations using Monte Carlo methods validate the theoretical bounds, confirming the tightness of the analytical models across diverse system configurations.